I had a situation a bit like yours about two years ago.
I bought a used motor scooter for my daughter to use while at college. When it was delivered I had the seller sign a bill of sale, and then he told me that he would bring me the title in a couple of days, because the woman he got the scooter from still had it. There was also an expired out-of-state license plate attached. According to him, the woman he got it from had received it from her sister as a gift, and when took possession she claimed she had temporarily misplaced the title. He had never titled or registered the scooter.
I looked up the scooter's VIN on one of those title and license plate search websites (paid a small fee for that) and found out that the real registered owner lived in the state where the license plate came from. I also discovered that the plate was issued for a different vehicle, a full size motorcycle.
At this point I was wondering whether I had stolen merchandise sitting in my driveway. But I still wanted the scooter.
It took several tries over the course of two weeks to finally get ahold of the woman, culminating in my tracking down her son and knocking on his door, whereupon he called her and I finally got to talk to her. She confirmed the story that I had been told and promised to look for the title.
Two weeks later she called and said she would have to get her sister to order a replacement title. But the sister no longer had the VIN or vehicle description. Fortunately, I had them written down in my folio.
The replacement title was not a priority for the sister. She could have gotten the replacement issued within 24 hours; she took a month. When it finally did arrive the sister had signed her name in the Seller block (whew!) but left the rest blank. The woman forwarded it straight to me without signing it herself.
Of course, I didn't have a Bill of Sale from the woman or her sister. I've been around the block enough times to know that the DMV office doesn't like non-routine transactions, so I called two privately owned auto title offices. One of them said that without a Bill of Sale I'd have to pay the tax and transfer fees based on the standard Blue Book value; the other one said they'd let me report what I actually paid, which was substantially less than Blue Book.
It's a good thing I received the replacement title. With the vehicle titled in another state, and without a dated Bill of Sale proving the transaction date, they were going to charge me a penalty for failure to timely re-register in state. But the replacement title had the date of issuance printed on it, and I was registering it as the new owner within the allowable window after that date.
So, nearly two months after I took delivery, I was finally able to bring the motor scooter to my daughter's college.